$\text F = \left[\begin{array}{rr}0 & 4 \\ 5 & 2\end{array}\right]$ and $\text D = \left[\begin{array}{rr}2 & 5 \\ 3 & 0\end{array}\right]$. Let $\text {H = FD}$. Find $\text H$. $ {H = }$
Solution: The Strategy When multiplying matrices, we should find each entry of the resulting product matrix separately. To find entry $(i,j)$ of the resulting product matrix, we calculate the vector dot product of row $i$ of the first matrix and column $j$ of the second matrix. [I don't know what "vector dot product" is!] Finding $\text {H}_{1,1}$ $\text{H}_{1,1}$ is the dot product of the first row of $\text{F}$ and the first column of $\text{D}$. $ \text {H}=\left[\begin{array}{rr}{0} & {4} \\ 5 & 2\end{array}\right]\left[\begin{array}{rr} {2} & 5 \\ {3} & 0\end{array}\right]$ Therefore, this is the appropriate calculation of $\text{H}_{1,1}$. $\begin{aligned}\text{H}_{1,1}&=(0,4)\cdot(2,3)\\\\ &=0 \cdot 2 + 4\cdot 3\\\\ &=12 \end{aligned}$ The other entries of $\text{H}$ can be found similarly. Try it yourself for $\text{H}_{2,1}$ What is the appropriate calculation of ${H}_{2,1}$ ? Choose 1 answer: Choose 1 answer: (Choice A) A $5 \cdot 5 + 2 \cdot 0 = 25$ (Choice B) B $5 \cdot 2 + 2 \cdot 3 = 16$ (Choice C) C $0 \cdot 5 + 4 \cdot 0 = 0$ Check Summary After calculating all the remaining entries of $\text{H}$, we get the following answer. $ \text {H}=\left[\begin{array}{rr}12 & 0 \\ 16 & 25\end{array}\right]$